In extremely large-scale multiple input multiple output (XL-MIMO) systems, near-field beam training is an essential way to acquire channel state information. To reduce the high training overhead brought by the additional distance dimension of the near-field codebook, some overhead-reduced near-field beam training schemes were proposed in the literature. However, existing schemes ignore the correlation between different near-field beams. In this paper, we propose a Bayesian regression-based near-field beam training scheme, which fully utilizes the correlation between near-field code-words to reduce the training overhead. Specifically, inspired by Bayesian regression, we model the received signal corresponding to different near-field codewords as a Gaussian process and determine the optimal codeword by iteratively updating the posterior distribution and designing the codeword searching order. Besides, different searching strategies are analysed and compared. The proposed scheme only requires searching for a few codewords instead of the entire codebook, which reduces the high training overhead. Simulation results verify the effectiveness of the proposed Bayesian regression-based near-field beam training scheme, which significantly reduces the training overhead while maintaining the high achievable rate performance.

Densifying multiple-input multiple-output (MIMO) has attracted much attention in recent years. The strong correlations among densifying antennas provide sufficient prior knowledge about channel state information (CSI), which inspires the careful design of observation matrices (e.g., transmit precoders and receive combiners) to boost channel estimation performance. To achieve this, this work proposes to jointly design the combiners and precoders by maximizing the mutual information between the received pilots and densifying MIMO channels. Particularly, a two-dimensional ice-filling (2DIF) algorithm is proposed, which is motivated by the fact that the eigenspace of MIMO channel covariance can be decoupled into two sub-eigenspaces. By properly setting the precoder and the combiner as the eigenvectors from these two sub-eigenspaces, the 2DIF promises to generate nearoptimal observation matrices for channel estimation. Simulation results demonstrate that, the proposed 2DIF method outperforms the state-of-the-art schemes in channel estimation accuracy.

By deploying a large number of antennas with subhalf- wavelength spacing in a compact space, dense array systems (DASs) can fully unleash the multiplexing and diversity gains of limited apertures. To acquire these gains, accurate channel state information acquisition is necessary but challenging due to the large antenna numbers. To overcome this obstacle, this paper reveals that designing the observation matrix to exploit the high spatial correlation of DAS channels is crucial for realizing near-optimal Bayesian channel estimation. Specifically, we prove that the observation matrix design for channel estimation is equivalent to a time-domain duality of point-to-point multipleinput multiple-output precoding, except for the change in the total power constraint on the precoding matrix to the pilot-wise discrete power constraint on the observation matrix. Inspired by Bayesian regression, a novel ice-filling algorithm is proposed to design amplitude-and-phase controllable observation matrices, and a majorization-minimization algorithm is proposed to address the phase-only controllable case. Particularly, we prove that the ice-filling algorithm can be interpreted as a “quantized” water-filling algorithm, wherein the latter’s continuous power-allocation process is converted into the former’s discrete pilot-assignment process. To support the near-optimality of the proposed designs, we provide comprehensive analyses on the achievable mean square errors and their asymptotic expressions. Finally, numerical results confirm that our proposed designs achieve the near-optimal channel estimation performance and outperform existing approaches significantly.

In extremely large-scale multiple input multiple output (XL-MIMO) systems, near-field beam training (NFBT) is an essential way to acquire channel state information (CSI) knowledge. To reduce the high training overhead caused by the distance dimension of the near-field codebook, some overhead-reduced NFBT schemes were proposed in the literature. However, existing schemes ignore the correlation between different near-field beams, which promises to provide prior knowledge for the reduction of training overhead. Aligned with this vision, this paper proposes a Bayesian regression (BAR)-based NFBT scheme, which fully utilizes the strong correlation between near-field codewords to achieve near-optimal and low-overhead NFBT. Specifically, inspired by Bayesian regression, we model the received signal corresponding to different codewords as a Gaussian process. Then, the optimal codeword can be determined by iteratively updating the posterior distribution and designing the codeword searching order. Besides, different codeword inference strategies are analyzed and compared. The proposed scheme only requires searching for a few codewords instead of the entire codebook thus avoiding the high training overhead. Simulation results verify that, compared to the existing schemes, the proposed scheme can significantly reduce the training overhead while maintaining a near-optimal achievable rate performance.

Fluid antenna systems (FASs) can reconfigure their antenna locations freely within a spatially continuous space. To keep favorable antenna positions, the channel state information (CSI) acquisition for FASs is essential. While some techniques have been proposed, most existing FAS channel estimators require several channel assumptions, such as slow variation and angular-domain sparsity. When these assumptions are not reasonable, the model mismatch may lead to unpredictable performance losses. In this paper, we propose the successive Bayesian reconstructor (S-BAR) as a general solution to estimate FAS channels. Unlike model-based estimators, the proposed S-BAR is prior-aided, which builds the experiential kernel for CSI acquisition. Inspired by Bayesian regression, the key idea of S-BAR is to model the FAS channels as a stochastic process, whose uncertainty can be successively eliminated by kernel-based sampling and regression. In this way, the predictive mean of the regressed stochastic process can be viewed as a Bayesian channel estimator. Simulation results verify that, in both model-mismatched and model-matched cases, the proposed S-BAR can achieve higher estimation accuracy than the existing schemes.

Fluid antenna systems (FASs) can reconfigure their locations freely within a spatially continuous space. To keep favorable antenna positions, the channel state information (CSI) acquisition for FASs is essential. While some techniques have been proposed, most existing FAS channel estimators require several channel assumptions, such as slow variation and angular-domain sparsity. When these assumptions are not reasonable, the model mismatch may lead to unpredictable performance loss. In this paper, we propose the successive Bayesian reconstructor (S- BAR) as a general solution to estimate FAS channels. Unlike model-based estimators, the proposed S- BAR is prior-aided, which builds the experiential kernel for CSI acquisition. Inspired by Bayesian regression, the key idea of S- BAR is to model the FAS channels as a stochastic process, whose uncertainty can be successively eliminated by kernel-based sampling and regression. In this way, the predictive mean of the regressed stochastic process can be viewed as the maximum a posterior (MAP) estimator of FAS channels. Simulation results verify that, in both model-mismatched and model-matched cases, the proposed S-BAR can achieve higher estimation accuracy than the existing schemes.

Extremely large-scale MIMO (XL-MIMO) is a promising technique for future 6G communications. The sharp increase in the number of antennas results in a transition of electromagnetic propagation from the far-field to the near-field. Due to the near-field effect, the exhaustive near-field beam training at all angles and distances requires very high overhead. The improved fast near-field beam training scheme based on time-delay structure can reduce the overhead, but it suffers from very high hardware costs and energy consumption caused by time-delay circuits. In this paper, we propose a near-field two dimension (2D) hierarchical beam training scheme to reduce the overhead without the need for extra hardware circuits. Specifically, we first formulate the multi-resolution near-field codewords design problem covering different angle and distance coverages. Next, inspired by phase retrieval problems in digital holography imaging technology, we propose a Gerchberg-Saxton (GS)-based algorithm to acquire the theoretical codeword by considering the fully digital architecture. Based on the theoretical codeword, an alternating optimization algorithm is proposed to acquire the practical codeword considering the hybrid digital-analog architecture. Finally, with the designed multi-resolution codebooks, we propose a near-field 2D hierarchical beam training scheme to significantly reduce the training overhead, which is verified by extensive simulation results.

Cooperation among entities within networks for information exchange and measurement is a promising paradigm for high-accuracy positioning in automated vehicles. However, due to imperfect clocks and inefficient wireless protocols, current cooperative positioning techniques have inadequate accuracy and timeliness. This paper presents a novel localization framework for connected automated vehicles (CAVs) capable of achieving high-accuracy relative positioning with high update rates. We design a signal-multiplexing network measuring (SNM) protocol to optimize the measurement update rates and propose new range estimations to achieve high-accuracy ranging against clock errors and mobility. Using range estimations, we develop a relative localization algorithm that leverages intra- and inter-node cooperation with coordinate reference alignment to reconstruct the geometric relationships among the nodes. Performance analyses and simulation results demonstrate that our method achieves high-accuracy positioning with timely updates, ensuring reliability and robustness in asynchronous vehicle localization.

The evolution of multi-input multi-output (MIMO) will develop toward extremely large-scale MIMO (XL-MIMO) for future 6G communications. With the extension of the antenna array, the electromagnetic propagation change from far-field to near-field. Because of the near-field effect, the exhaustive near-field beam training scanning all angles and distances involves very high overhead. The existing fast near-field beam training scheme with extra time-delay circuits can reduce the overhead, but it suffers from very high hardware costs and energy consumption. To solve this issue, we propose a low-overhead near-field two dimension (2D) hierarchical beam training after carefully designing the near-field multi-resolution codebooks. Specifically, we first formulate the problem of designing near-field multi-resolution codewords, which have various angle coverage and distance coverage. Next, we propose a Gerchberg-Saxton (GS)-based algorithm to obtain the theoretical codeword by considering the ideal fully digital architecture, and an alternating optimization algorithm is then proposed to acquire the practical codeword by considering the hybrid digital-analog architecture. Finally, we generate multi-resolution codebooks and propose a near-field 2D hierarchical beam training scheme. Simulation results demonstrate that the proposed scheme can provide a tradeoff between the achievable rate performance and overhead in near-field XL-MIMO beam training.

Extremely large-scale multiple-input multiple-output (XL-MIMO) is a promising technology for future 6G communications. To realize effective precoding, channel estimation schemes are essential to acquire precise channel state information (CSI), while most existing schemes work relying on the spatial stationary assumption. In XL-MIMO systems, however, the spatial non-stationary effect naturally exists. Such effect can hardly be recognized by existing channel estimation schemes, leading to a severe accuracy loss of channel estimation. To address this problem, in this paper, we study the spatial non-stationary channel estimation for XL-MIMO systems. Specifically, we propose a group time block code (GTBC) based signal extraction scheme. The key idea is to artificially create and exploit the time-domain relevance of non-stationary effect, which allows XL-MIMO to recognize such effect in the space domain. In this way, the spatial non-stationary channel is converted to a series of spatial stationary channels. To effectively estimate these channels, a GTBC-based polar-domain simultaneous orthogonal matching pursuit (GP-SOMP) algorithm is proposed as a solution. Simulation results reveal that the proposed GP-SOMP algorithm can recognize the spatial non-stationary effect in XL-MIMO systems and realize a much more accurate channel estimation than existing schemes.

In recent years, thanks to the advances in meta-materials, the concept of continuous-aperture MIMO (CAP-MIMO) is reinvestigated to achieve improved communication performance with limited antenna apertures. Unlike the classical MIMO composed of discrete antennas, CAP-MIMO has a quasi-continuous antenna surface, which is expected to generate any current distribution (i.e., pattern) and induce controllable spatial electromagnetic (EM) waves. In this way, the information is directly modulated on the EM waves, which makes it promising to approach the ultimate capacity of finite apertures. The pattern design is the key factor to determine the communication performance of CAP-MIMO, but it has not been well studied in the literature. In this paper, we develop pattern-division multiplexing (PDM) to design the patterns for CAP-MIMO. Specifically, we first study and model a typical multi-user CAP-MIMO system, which allows us to formulate the sum-rate maximization problem. Then, we develop a general PDM technique to transform the design of the continuous pattern functions to the design of their projection lengths on finite orthogonal bases, which can overcome the challenge of functional programming. Utilizing PDM, we further propose a block coordinate descent (BCD) based pattern design scheme to solve the formulated sum-rate maximization problem. Simulation results show that, the sum-rate achieved by the proposed scheme is higher than that achieved by benchmark schemes, which demonstrates the effectiveness of the developed PDM for CAP-MIMO.

Traditional channel capacity based on the discrete spatial dimensions mismatches the continuous electromagnetic fields. For the wireless communication system in a limited region, the spatial discretization may results in information loss because the continuous field can not be perfectly recovered from the sampling points. Therefore, electromagnetic information theory based on spatially continuous electromagnetic fields becomes necessary to reveal the fundamental theoretical capacity bound of communication systems. In this paper, we propose analyzing schemes for the performance limit between continuous transceivers. Specifically, we model the communication process between two continuous regions by random fields. Then, for the white noise model, we use Mercer expansion to derive the mutual information between the source and the destination. For the close-form expression, an analytic method is introduced based on autocorrelation functions with rational spectrum. Moreover, the Fredholm determinant is used for the general autocorrelation functions to provide the numerical calculation scheme. Further works extend the white noise model to colored noise and discuss the mutual information under it. Finally, we build an ideal model with infinite-length source and destination which shows a strong correpsondence with the time-domain model in classical information theory. The mutual information and the capacity are derived through the spatial spectral density.

As a revolutionary paradigm for controlling wireless channels, reconfigurable intelligent surfaces (RISs) have emerged as a candidate technology for future 6G networks. However, due to the “multiplicative fading” effect, the existing passive RISs only achieve limited capacity gains in many scenarios with strong direct links. In this paper, the concept of active RISs is proposed to overcome this fundamental limitation. Unlike passive RISs that reflect signals without amplification, active RISs can amplify the reflected signals via amplifiers integrated into their elements. To characterize the signal amplification and incorporate the noise introduced by the active components, we develop and verify the signal model of active RISs through the experimental measurements based on a fabricated active RIS element. Based on the verified signal model, we further analyze the asymptotic performance of active RISs to reveal the substantial capacity gain they provide for wireless communications. Finally, we formulate the sum-rate maximization problem for an active RIS aided multi-user multiple-input single-output (MU-MISO) system and a joint transmit beamforming and reflect precoding scheme is proposed to solve this problem. Simulation results show that, in a typical wireless system, passive RISs can realize only a limited sum-rate gain of 22%, while active RISs can achieve a significant sum-rate gain of 130%, thus overcoming the “multiplicative fading” effect.

Reconfigurable intelligent surfaces (RISs) have emerged as a candidate technology for future 6G networks. However, due to the “multiplicative fading” effect, the existing passive RISs only achieve a negligible capacity gain in environments with strong direct links. In this paper, the concept of active RISs is studied to overcome this fundamental limitation. Unlike the existing passive RISs that reflect signals without amplification, active RISs can amplify the reflected signals via amplifiers integrated into their elements. To characterize the signal amplification and incorporate the noise introduced by the active components, we verify the signal model of active RISs through the experimental measurements on a fabricated active RIS element. Based on the verified signal model, we formulate the sum-rate maximization problem for an active RIS aided multi-user multiple-input single-output (MU-MISO) system and a joint transmit precoding and reflect beamforming algorithm is proposed to solve this problem. Simulation results show that, in a typical wireless system, the existing passive RISs can realize only a negligible sum-rate gain of 3%, while the active RISs can achieve a significant sum-rate gain of 62%, thus over coming the “multiplicative fading” effect. Finally, we develop a 64-element active RIS aided wireless communication prototype, and the significant gain of active RISs is validated by field test.

In recent years, continuous-aperture multiple-input multiple-output (CAP-MIMO) is reinvestigated to achieve improved communication performance with limited antenna apertures. Unlike the classical MIMO composed of discrete antennas, CAP-MIMO has a continuous antenna surface, which is expected to generate any current distribution (i.e., pattern) and induce controllable spatial electromagnetic waves. In this way, the information can be modulated on the electromagnetic waves, which makes it promising to approach the ultimate capacity of finite apertures. The pattern design for CAP-MIMO is the key factor to determine the communication performance, but it has not been well studied in the literature. In this paper, we propose the pattern-division multiplexing to design the patterns for CAPMIMO. Specifically, we first derive the system model of a typical multi-user CAP-MIMO system, which allows us to formulate the sum-rate maximization problem. Then, we propose a general pattern-division multiplexing technique to transform the design of continuous pattern functions to the design of their projection lengths on finite orthogonal bases. Based on this technique, we further propose a pattern design scheme to solve the formulated sum-rate maximization problem. Simulation results show that, the sum-rate achieved by the proposed scheme is about 260% higher than that achieved by the benchmark scheme.

Shannon-Hartley theorem can accurately calculate the channel capacity when the signal observation time is infinite. However, the calculation of finite-time mutual information, which remains unknown, is essential for guiding the design of practical communication systems. In this paper, we investigate the mutual information between two correlated Gaussian processes within a finite-time observation window. We first derive the finite-time mutual information by providing a limit expression. Then we numerically compute the mutual information within a single finite-time window. We reveal that the number of bits transmitted per second within the finite-time window can exceed the mutual information averaged over the entire time axis, which is called the exceed-average phenomenon. Furthermore, we derive a finite-time mutual information formula under a typical signal autocorrelation case by utilizing the Mercer expansion of trace class operators, and reveal the connection between the finite-time mutual information problem and the operator theory. Finally, we analytically prove the existence of the exceed-average phenomenon in this typical case, and demonstrate its compatibility with the Shannon capacity.

Extremely large-scale MIMO (XL-MIMO) communication is a promising technology to improve the capacity for future 6G networks. With a very large number of antennas, the near-field property of XL-MIMO systems becomes significant. Unlike the classical far-field line-of-sight (LoS) channel with only one available data stream, significantly increased degrees of freedom (DoFs) are available in the near-field LoS channel. However, limited by the small number of radio frequency (RF) chains, the existing hybrid precoding architecture widely used for 5G is not able to fully utilize the extra DoFs in the near-field region. In this paper, to exploit the near-field effect as a new possibility for capacity improvement, the distance-aware precoding (DAP) architecture is developed, where each RF chain can be flexibly configured to active or inactive according to the distance-related DoFs. Moreover, based on the developed DAP architecture, a DAP algorithm is proposed to optimize the number of activated RF chains and precoding matrices to match the increased DoFs. Finally, simulation results verify that, the proposed DAP scheme can efficiently utilize the extra DoFs in the near-field region to improve the spectrum efficiency.

Large-scale antenna arrays employed by the base station (BS) constitute an essential next-generation communications technique. However, due to the constraints of size, cost, and power consumption, it is usually considered unrealistic to use a large-scale antenna array at the user side. Inspired by the emerging technique of reconfigurable intelligent surfaces (RIS), we firstly propose the concept of user-specific RIS (US-RIS) for facilitating the employment of a large-scale antenna array at the user side in a cost- and energy-efficient way. In contrast to the existing employments of RIS, which belong to the family of base-station-specific RISs (BSS-RISs), the US-RIS concept by definition facilitates the employment of RIS at the user side for the first time. This is achieved by conceiving a multi-layer structure to realize a compact form-factor. Furthermore, our theoretical results demonstrate that, in contrast to the existing single-layer structure, where only the phase of the signal reflected from RIS can be adjusted, the amplitude of the signal penetrating multi-layer US-RIS can also be partially controlled, which brings about a new degree of freedom (DoF) for beamformer design that can be beneficially exploited for performance enhancement. In addition, based on the proposed multi-layer US-RIS, we formulate the signal-to-noise ratio (SNR) maximization problem of US-RIS-aided communications. Due to the non-convexity of the problem introduced by this multi-layer structure, we propose a multi-layer transmit beamformer design relying on an iterative algorithm for finding the optimal solution by alternately updating each variable. Finally, our simulation results verify the superiority of the proposed multi-layer US-RIS as a compact realization of a large-scale antenna array at the user side for uplink transmission.

Precise range information is essential for high-precision network localization, where clock drifts will severely degrade the ranging accuracy. Two-way ranging methods are commonly adopted to mitigate those effects in localization networks but requiring a large amount of signal transmission to measure the distance between all pairs of nodes. This paper establishes a network localization framework, which fully mitigates clock drifts using only a minimum number of signal transmissions. The enabler is the proposed signal-multiplexing network ranging (SM-NR) method that minimizes communication overhead via signal multiplexing and eliminates clock drifts by exploiting the interconnections of timestamps. The proposed localization framework also allows some nodes to work in silent mode, of which the positions can be precisely determined without extra ranging signal transmissions. Simulation results show that the proposed algorithm can achieve high-precision localization in the presence of clock drifts with minimum signal overhead.

Massive multiple-input multiple-output (MIMO) with a large-scale antenna array at the base station (BS) side is one of the most essential techniques for 5G wireless communications. However, due to the forbidden hardware cost and mismatched size, it is physically limited to deploy massive MIMO at the user side. To break this limitation, inspired by the promising technique called reconfigurable intelligent surface (RIS), we firstly propose the concept of user-side RIS (US-RIS) which is a cost- and energy-efficient realization for large-scale array at the user side. Different from the existing RISs that work as base-station-side RISs (BSS-RISs), US-RIS is the first usage of RIS at the user side. Then, we propose a novel architecture of user with the aid of US-RIS with a multi-layer structure for compact implementation. Based on the proposed multi-layer US-RIS, we formulate the signal-to-noise ratio (SNR) maximization problem in the US-RIS-aided communications. To tackle the challenge of solving this non-convex problem, we propose a multi-layer precoding design that can obtain the optimal parameters at transceivers and US-RIS by iterative optimization. Finally, simulation results are shown to verify the practicability and superiorities of the proposed multi-layer US-RIS as a realization of the large-scale array at the user side.

With the ability to overcome the inter-cell interferences, cell-free network is a promising network paradigm to achieve high spectrum efficiency for future 6G communications. However, the increasing number of distributed base stations in cell-free network introduces very high power consumption. To address this issue, inspired by the reconfigurable intelligent surface (RIS) technique with low power consumption, the concept of RIS-aided cell-free network has been recently proposed to improve the spectrum efficiency at a low cost of power consumption. In this paper, we take a further step to investigate the energy-efficiency fairness (EEF) of RIS-aided cell-free network. Specifically, we formulate the precoding design problem to maximize the energy efficiency of the worst user in a wideband RIS-aided cell-free network. To solve this problem, we then propose an iterative precoding algorithm by using Lagrangian transform and fractional programming (FP) to tackle the highly decoupled optimization objective. Through alternatingly solving subproblems of subcarrier assignment, power allocation, combining, and precoding, the objective will finally converge. Simulation results demonstrate the effectiveness of the proposed precoding algorithm, and the energy efficiency of users in cell-free network can be efficiently increased by the aid of RISs.